Page 4 - Xl-CH-16-LESSON NOTE

( )
P(E) = = =
( )

Example: 2 A card is selected from a pack of 52 cards
(a) How many points are there in the simple space?
(b) Calculate the probability that the card is an ace of spades.
(c) Calculate the probability that the card is (i) an ace (ii) black card

Solution:- One card is drawn from the pack of 52 cards.

(a) One card is drawn from the pack of 52 cards.
⇒ Number of points in the sample space S = n (S) = 52
(b) Let A be the event of drawing an ace of spades. Now there is only one space of
spade.
1
Therefore P (A) =
52
(c) (i) Let B be the event of drawn an ace. Now there are four aces
4 1
Therefore P (B) = =
52 13
(ii) Let C be the event of drawing a black card. Now there are 26 black cards
26 1
Therefore P(C) = =
52 2
ADDITION THEROREM ON PROBABILITY:

If A and B are two events associated with a random experiment then

( ∪ ) = ( ) + ( ) − ( ∩ )

Example: In class XI of a school 40% of the students study Mathematics and 30% study Biology,
10% of the class study both Mathematics and Biology. Find the probability that he will be
studying Mathematics or Biology.

40 2 30 3
Ans : P(A) = = and P(B) = = =
100 5 100 5
10
( ∩ ) =
100

We know that ( ∪ ) = ( ) + ( ) − ( ∩ )

2 3 1 3
= + − =
5 5 10 5